Questions tagged [greedy-algorithms]
Questions about algorithms that make at each step the locally optimal choice.
349
questions
6
votes
2answers
6k views
Greedy and backtracking solutions to an arrangement problem with constraints
I'm revising for my finals. I have found a pattern in past papers in terms of a recurring question, reworded coming up every year. But I've no idea what the marker actually wants... I've asked class ...
1
vote
1answer
865 views
Find a quarrel-free seating order with a greedy algorithm [duplicate]
I'm revising for an Algorithms exam and looking at a sample question it says :
A group of n teenagers $t_1, \dots, t_n$ are to sit in a single row of n chairs watching a particulary boring comedy ...
2
votes
1answer
164 views
What is the optimal strategy for filtering a large collection of items with multiple filter functions?
I have a large collection of items, and a list of independent filters (boolean functions). I want to find the collection of items that pass all of my filters as quickly as possible. This must involve ...
4
votes
2answers
2k views
Greedy proof: Correctness versus optimality
I am really confused after surveying a bunch of material online about correctness versus optimality proof for greedy algorithms. Some website even uses both correctness and optimal in the same ...
5
votes
2answers
667 views
Do all greedy algorithm produce just the first solution, no matter how bad it is?
In all the exampls of the greedy algorithms I've seen so far, such as activity selection problem and unit-sized set coverage problem, the algorithm is usually very simple and intuitive and returns the ...
1
vote
2answers
364 views
Find the coins required which sum to S
Given a list of $N$ coins, their values $V_1, V_2, \cdots , V_N$, and a parameter of a total sum $S$. Find the coins the sum of which is S (we can use each coin at most once).
I was recently studying ...
3
votes
1answer
254 views
Does a greedy task selection algorithm find a c-approximate solution?
I was told this question may be better suited here.
A scheduling problem can be stated as: Given a set
$\{(s_i,f_i)\}_{1\le i\le n}\}$ of tasks identified by their start and
end times, choose ...
-1
votes
1answer
178 views
How do you come up with greedy algorithm for deadline scheduling when comparing x_subscript(i) and y_subscript(k)?
So there are two boxing teams, my team A and the opposing team B, each with m boxers. Based on the player's ranking of skill, x_subscript(i) being the ranking for ith boxer for team A and y_subscript(...
2
votes
2answers
1k views
minimum spanning tree and minimum heavyweight spanning tree [duplicate]
a minimum heavyweight spanning tree is a spanning tree in which the heaviest edge is as light as possible.
Formally,
input : given connected undirected weighted graph, $G$.
output : a spanning tree $T$...
-1
votes
1answer
117 views
Minimising two maximum edges in s-t path
I've been trying to solve the following problem:
Problem is the following:
Given a graph and a pair of nodes $s$, $t$ you have to find the path from $s$ to $t$ which minimises the sum of its two ...
-2
votes
1answer
1k views
How to figure out the minimal number of colors needed to color specific given graphs?
I found this question on the net and I'm wondering what is the process for answering such questions? I assume there is some formula that works for all graphs?
1.a.
Consider the undirected graph with ...
3
votes
1answer
2k views
Fast algorithm for matrix chain multiplication in special case
An exercise from the book Foundations of Algorithms Using Java Pseudocode:
Write an efficient algorithm that will find an optimal order for
multiplying $n$ matrices $A_1 \times A_2 \times \ldots \...
1
vote
2answers
187 views
Greedily Schedule Events based on value/hours
Suppose we are given a list of $n$ events $E = \{E_1, E_2, \ldots, E_n\}$ where each $E_i$ is represented by $(s_i, h_i, v_i)$ or $(start, hours, value)$. So if you attend an entire event that lasts ...
4
votes
2answers
359 views
Minimizing Cost by minimizing delay
There is a complete binary tree with its leaves as components of some system
The values from one node to another gives propagation time for a signal to propagate from one junction to another
For the ...
1
vote
0answers
57 views
Conjecture about a matrix column swapping challenge problem
So here is the challenge problem statement: https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1512
Basically, given a 0/1 matrix, you ...
1
vote
1answer
2k views
Dynamic programming VS Greedy Algroithms [closed]
I have two True or False questions in my practice test that are related but I am unsure about:
...
1
vote
3answers
5k views
Correctness proof of greedy algorithm for 0-1 knapsack problem
We have a 0-1 knapsack in which the increasing order of items by weight is the same as the decreasing order of items by value. Design a greedy algorithm and prove that the greedy choice guarantees an ...
1
vote
0answers
48 views
How to maximize the number of buyers in a shop?
There is a shop which consists of N items and there are M buyers. Each buyer wants to buy a specific set of items. However, the cost of all transactions is same irrespective of the number of items ...
2
votes
1answer
840 views
GSAT incompleteness example
The GSAT (Greedy Satisfiability) algorithm can be used to find a solution to a search problem encoded in CNF. I'm aware that since GSAT is greedy, it is incomplete (which means there would be cases ...
-1
votes
2answers
2k views
Proof of Correctness of Prim's algorithm [duplicate]
what is the reason for the correctness proof of Prim's Algorithm for the undirected case cannot carry over to the directed case?
Is it because of after any number of steps, $S$ might not be in a sub ...
-1
votes
1answer
2k views
Minimal Spanning tree and Prim's Algorithm
Is there any example that anybody could come up with that shows Prim's algorithm does not always give the correct result when it comes knowing the minimal spanning tree.
0
votes
2answers
1k views
Algorithm for sorting with constraints
I've got 30 elements which has to be grouped/sorted into 10 ordered 3-tuple.
There are several rules and constraints about grouping/sorting.
For example: Element $A$ must not be in the same tuple ...
2
votes
1answer
583 views
Finding an instance of an n-element set cover
Below is a homework problem where we have been asked to alter a greedy algorithm to return n element instance of a set problem. The original algorithm is also below. I was thinking that I could alter ...
2
votes
0answers
733 views
Single machine job scheduling (Greedy heuristic)
Here is a variation of a job-scheduling Problem.
Let $J = \{j_1,...j_n\}$ be a set of Jobs for $1 \leq i \leq n$. Given Job length $|j_i|\in \mathbb{N}$, deadline $f_i \in \mathbb{N}$, profit $p_i \ge ...
1
vote
0answers
842 views
Fast algorithm for finding a minimum cost path through points in the plane
Consider the following problem:
There are $n$ points in the plane.
Starting from one of them I want to visit each of them once (except the starting node which has to be visited twice) but in a way ...
-1
votes
1answer
2k views
How to minimize the sum of difference of element in sub-sequence of array of length k from given sequence of length n
How to minimize the sum of difference of element in sub-sequence of array of length k from given sequence of length n ?
for example : for n=10
1
2
3
4
10
20
30
40
100
200
the sub-sequence of length ...
3
votes
1answer
6k views
How to implement GREEDY-SET-COVER in a way that it runs in linear time [closed]
This is an exercise in the book Introduction to Algorithm, 3rd Edition.
The original question is:
Show how to implement GREEDY-SET-COVER in such a way that it runs in time $O(\sum_{S\in\mathcal{F}}|...
2
votes
0answers
674 views
Other greedy choices to solve activity selection problem
I have been studying about activity-selection-problem and the solution of greedy choice I came across is to select the activity that finishes in the earliest among the present activities.
But surely ...
3
votes
1answer
148 views
Generalizing the linear subset scan algorithm to a wider class of objective functions, maybe by finding a paper
Given a list of pairs $(a_1,b_1),\ldots,(a_n,b_n)$, where all $a_i \geq 0$ and all $b_i > 0$, my general problem is when we can use linear subset scan (described below) to solve the optimization ...
4
votes
2answers
29k views
Time complexity of a backtrack algorithm
I've developed the following backtrack algorithm, and I'm trying to find out it time complexity.
A set of $K$ integers defines a set of modular distances between all pairs of them. In this
algorithm, ...
1
vote
1answer
12k views
Proving greedy choice property of fractional knapsack
A typical way of proving the greedy choice property of the fractional knapsack problem is as follows:
From Slide 5 of this link:
Given: A set of items $I = \{I_1,I_2..I_n\}$ with weights $\{w_1,w_2 ....
15
votes
2answers
13k views
Correctness-Proof of a greedy-algorithm for minimum vertex cover of a tree
There is a greedy algorithm for finding minimum vertex cover of a tree which uses DFS traversal.
For each leaf of the tree, select its parent (i.e. its parent is in minimum vertex cover).
For each ...
2
votes
1answer
1k views
Solving a variant of interval scheduling problem [duplicate]
I am trying to solve a problem of finding compatible jobs set using greedy algorithm. However, I am not sure if greedy algorithm can solve this problem or I need to perform another approach.
I have a ...
4
votes
1answer
616 views
Issues with using greedy algorithm (Interval scheduling variant)
I am trying to solve a problem of finding incompatible jobs set using greedy algorithm. However, I am not sure if greedy algorithm can solve this problem or I need to perform another approach.
I have ...
3
votes
3answers
9k views
Fractional Knapsack in linear time
How to solve fractional knapsack in linear time? I found this on Google but don't really understand it.
Choose element $r$ at random from $R$ (set of profit/weight ratios)
Determine
$R_1 = \{ p_i / ...
8
votes
4answers
9k views
Find non-overlapping scheduled jobs with maximum cost
Given a set of n jobs with [start time, end time, cost] find a subset so that no 2 jobs overlap and the cost is maximum.
Now I'm not sure if a greedy algorithm will do the trick. That is, sort by ...
5
votes
1answer
358 views
Single machine job scheduling to minimize weighted sum of completion time
Given $n$ jobs, schedule them such that the weighted sum is minimum.
weighted minimum sum S for the schedule $\sigma = \{ J_1, J_2, ... J_n \}$ is given by :
$S = \sum_{1\leqq i \leqq n} w_i C_i$ ...
2
votes
2answers
3k views
Greedy Optimum Dominating Set For A Tree
I am trying to figure out a greedy algorithm that finds the optimum (minimum) dominating set for any tree in linear time.
So a greedy algorithm to find a dominating set for a general graph is not ...
3
votes
1answer
138 views
Show that approximation ratio for a convex hull algorithm is $\pi/2$
Facts: n points in the plane, each has one of k colors, all k colors are represented.
Problem: You wish to select k points, one of each color, such that the perimeter of the convex hull is as small ...
9
votes
1answer
211 views
Fixed-length decision-tree-like feature selection to minimize average search performance
I have a complex query $Q$ used to search a dataset $S$ to find $H_\text{exact} = \{s \in S \mid \text{where $Q(s)$ is True}\}$. Each query takes on average time $t$ so the overall time in the linear ...
0
votes
1answer
2k views
Greedy algorithms tutorial
Could anyone point me to simple tutorial on greedy algorithm for Minimum Spanning tree - Kruskal's and Prims' Method
I am looking for a tutorial which
does not include all the mathematical ...
28
votes
1answer
30k views
When can a greedy algorithm solve the coin change problem?
Given a set of coins with different denominations $c1, ... , cn$ and a value v you want to find the least number of coins needed to represent the value v.
E.g. for the coinset 1,5,10,20 this gives 2 ...
4
votes
1answer
564 views
Why do the swap step in Prim's algorithm for minimum spanning trees?
I was watching the video lecture from MIT on Prim's algorithm for minimum spanning trees.
Why do we need to do the swap step for proving the theorem that if we choose a set of vertices in minimum ...
7
votes
1answer
942 views
Greedy choice and matroids (greedoids)
As I was going through the material about the greedy approach, I came to know that a knowledge on matroids (greedoids) will help me approaching the problem properly. After reading about matroids I ...
7
votes
2answers
526 views
Balanced weighting of edges in cactus graph
Given a cactus, we want to weight its edges in such a way that
For each vertex, the sum of the weights of edges incident to the vertex is no more than 1.
The sum of all edge weights is maximized.
...
2
votes
2answers
1k views
“Flow layouts” inside a GUI — how do I come up with a good algorithm?
I was trying to write some simple code for a "flow layout" manager and what I came up with initially was something like the following (semi-pseudocode):
...
1
vote
0answers
51 views
How to use greedy algorithm to solve this? [duplicate]
Possible Duplicate:
How to use greedy algorithm to solve this?
You are given $n$ integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ ...
21
votes
4answers
2k views
How to use a greedy algorithm to find the non-decreasing sequence closest to the given one?
You are given n integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ between $0$ and $l$ with the requirement that the $b_i$'s form a non-...
23
votes
1answer
1k views
How fundamental are matroids and greedoids in algorithm design?
Initially, matroids were introduced to generalize the notions of linear independence of a collection of subsets $E$ over some ground set $I$. Certain problems that contain this structure permit greedy ...
